Let x0 of type ι be given.

Let x1 of type ι be given.

Let x2 of type ι be given.

Let x3 of type ι be given.

Apply unknownprop_b456609235d152f08bccfce314d541d7c44f3716137c00b0ce21cf467ba83d17 with 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))), λ x4 . If_i (x4 = 4a7ef..) x0 (If_i (x4 = 4ae4a.. 4a7ef..) x1 (If_i (x4 = 4ae4a.. (4ae4a.. 4a7ef..)) x2 x3)), 4ae4a.. 4a7ef.., λ x4 x5 . x5 = x1 leaving 2 subgoals.

The subproof is completed by applying unknownprop_9ec656cf0d83e7858e314f8d14d34003f98b73077d45230a446ec386d304d5f4.

Apply If_i_0 with 4ae4a.. 4a7ef.. = 4a7ef.., x0, If_i (4ae4a.. 4a7ef.. = 4ae4a.. 4a7ef..) x1 (If_i (4ae4a.. 4a7ef.. = 4ae4a.. (4ae4a.. 4a7ef..)) x2 x3), λ x4 x5 . x5 = x1 leaving 2 subgoals.

The subproof is completed by applying unknownprop_24ff2ea632296eb0012bd83ffdc0e75761169422164b438efe0673b96d912be0.

Let x4 of type ι → ι → ο be given.

The subproof is completed by applying H0.

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Proofgold Proof